MEN* OF MATHEMATICS
the wave mechanics associated with the modern quantum
theory and the theory of atomic structure. It may be recalled
that Newton had favoured an emission, or corpuscular, theory
oflight. while Huygens and his successors up to almost our own
time sought to explain the phenomena oflight wholly by means
of a wave theory. Both points of view were united and, in a
purely mathematical sense, reconciled in the modern quantum
theory, which came into being in 1925-6. In 1884, when he was
twenty-eight, Hamilton realized his ambition of extending the
principles which he had introduced into optics to the whole of
dynamics.
Hamilton's theory of rays, shortly after its publication when
its author was but twenty-seven, had one of the promptest and
most spectacular successes of any of the classics of mathe-
matics. The theoiy purported to deal with phenomena of the
actual physical universe as it is observed in everyday life and
in scientific laboratories. Unless any such mathematical theory
is capable of predictions which experiments later verify, it is no
better than a concise dictionary of the subject it systematizes,
and it is almost certain to be superseded shortly by a more
imaginative picture which does not reveal its whole meaning at
the first glance. Of the famous predictions which have certified
the value of truly mathematical theories in physical science, we
may recall three: the mathematical discovery by John Couch
Adams (1S1&-92) and Urbain-Jean-Joseph Leverrier (1811-77)
of the planet Neptune, independently and almost simulta-
neously in 1845, from an analysis of the perturbations of the
planet Uranus according to the Newtonian theory of gravita-
tion; the mathematical prediction of wireless waves by James
Clerk Maxwell (1831-79) in 1864, as a consequence of his own
electromagnetic theory of light; and finally, Einstein's predic-
tion in 1915-1G, from his theory of general relativity, of the
deflection of a ray of light in a gravitational field, first con-
firmed by observations of the solar eclipse on the historic
29 May 1919, and his prediction, also from his theory, that the
spectral lines in light issuing from a massive body would be
shifted by an amount, which Einstein stated, toward the red
end of the spectrum ~ also confirmed. The last two of these
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